A powerboat, starting from rest, maintains a constant acceleration

1. The problem statement, all variables and given/known data
A powerboat, starting from rest, maintains a constant acceleration. After a certain time t, its displacement and velocity are r and v. At time 2t, what would be its displacement and velocity, assuming the acceleration remains the same?
a) 2r and 2v
b) 2r and 4v
c) 4r and 2v
d) 4r and 4v

So you got ## v_1 = at ## and ## r_1 = at^2/2 ##. You have further found at ##2t##, ##v_2 = a(2t)## and ##r_2 = a(4t^2)/2##. All that you need to do is express ##v_2## via ##v_1## and ##r_2## via ##r_1##.

So you got ## v_1 = at ## and ## r_1 = at^2/2 ##. You have further found at ##2t##, ##v_2 = a(2t)## and ##r_2 = a(4t^2)/2##. All that you need to do is express ##v_2## via ##v_1## and ##r_2## via ##r_1##.